1. Field of the Invention
The present invention relates to a mask design technology and more particularly relates to a mask design method, a program therefore, and a mask design system.
2. Description of Related Art
The entire contents of US Patent applications identified by Ser. Nos. 12/334,482, 12/334,488 each filed on Dec. 14, 2008; Ser. No. 12/334,485 filed on Dec. 14, 2008; and the entire contents of U.S. Pat. No. 8,108,802 issued on Jan. 31, 2012; and of U.S. Pat. No. 7,057,709 issued on Jun. 6, 2006; may be incorporated herein as references.
Minimum printed feature sizes in semiconductor devices become finer due to continuous requirements for ever higher performance and faster operation of the devices while reducing space consumption of information processing apparatuses. Thus, the minimum feature size of state of the art semiconductor devices almost reaches to about 22 nm or less. Masks having patterns of structures for semiconductor devices may be used for photolithography of layers included in semiconductor devices. Patterns for forming a semiconductor device are provided by the mask so as to expose the patterns of the mask to an adequate photo-imaging technology, including immersion exposure technologies.
As feature sizes become finer and finer, the patterns formed in the mask may become designed by several techniques. For example, Optical Proximity Correction (OPC) technology, rule-based topology modification and model-based topology modification, and so-called inverse lithography technology (ILT); hereafter, the ILT technologies are simply referred to as ILT and as Source Mask Optimization (SMO) technology. The terms ILT and SMO are regarded here as interchangeable, and either term can be employed regardless of whether the source is optimized along with the mask.
Since OPC uses polygon domain and counter-biases the mask iteratively, it does not allow the modification of topology during optimization. Polygon domain, also referred to as spatial domain, refers to a mask representation based on polygons that have approximately the same shape as the apertures in the mask blank film. They are fabricated in a manufactured mask, with the location of the polygon edges serving as variables that define the mask. The polygon apertures typically have a transmission of 1, and the mask regions surrounding the polygons have the same transmission as the mask blank film.
In the common case of so-called binary masks, the mask blank transmission is approximately 0. In some cases the mask blank may have a transmission other than 0, and the transmission may be phase-shifted relative to the polygon transmission. So-called tri-tone masks may contain two kinds of aperture, each having a different transmission value. But in general, OPC adjusts the edge locations within each polygon to counter-bias the distortions in printed pattern edges, and it does so without changing the topology of the mask polygons. Polygon domain ILT or SMO uses optimization to determine the positions of the mask polygon edges, but during polygon domain optimization these techniques again leave the polygon topology unchanged.
The fixed topology limits optimization performance. The rule-based topology modification technology becomes less effective in the fabrication of state of the art semiconductor devices and human intuition may not provide an acceptable solution for the mask pattern. The ILT or SMO therefore often uses spatial frequency or transmission frequency analysis in the initial optimization of the optical domain.
Optical domain refers to a mask representation in which the mask variables essentially represent the amplitude of the light that transmits through the mask. The amplitudes used by ILT or SMO may be taken in a plane immediately past the mask, in which case they essentially represent the transmission of the mask, or they may be taken in the pupil of the projection lens, which collects the transmitted light and images it onto the semiconductor device substrate. Photolithographic lenses are almost always telecentric, in which case the pupil is planar, and for convenience the pupil is referred to as the pupil plane in the general case. The plane adjacent to the mask through which light exits is the object plane. The pupil plane amplitudes are related to the object plane amplitudes by Fourier-transformation in the usual case of scalar mask variables.
Likewise, the band-limited portion of the object plane amplitudes will be the inverse Fourier-transform (iFT) of the collected pupil amplitudes, and in some forms of SMO the optical variables only include light components that are captured by the projection lens. It should be noted that this collection process by the lens constitutes a band-limiting or filtering process. Those skilled in the art will recognize that it is also possible to use a convention in which the roles of the transform and inverse transform are reversed, but for simplicity such a convention will not be considered in the discussion below.
To distinguish these Fourier-transformations in the physical space of a lens system from the temporal Fourier-transformations that are commonly used in other electrical engineering contexts, the optical variables in ILT and SMO are conventionally said to comprise spatial frequencies. An optimization of the optical variables is sometimes referred to as an optimization in the spatial frequency domain, often referred to more briefly as a frequency domain optimization. The term frequency domain is sometimes employed in SMO regardless of whether the light amplitudes are measured in the pupil plane or the object plane, but this usage is not universal.
Likewise, the term spatial domain is sometimes used in SMO to refer to optimization of the polygonal shapes of mask apertures, though again this usage is not universal. In most of this document the terms frequency domain and spatial domain will be avoided since their usage varies in the literature. However, the acronyms FDJO and SDJO will be retained, as abbreviations that refer to joint optimization of mask variables and source variables, with the mask variables being defined in the optical domain for FDJO, and in the polygon domain for SDJO.
During an ILT or SMO flow, an optimizer may be used to control the gridded amplitude of the light transmitted through the mask. The mask optical variables in ILT may be the transmissions of the grid boxes, i.e. pixels, or they may be the values of the transmitted optical field at the points of a sampling grid. This light is optimized in the optical domain, and so can be referred to in SMO as a frequency domain optimization. In SMO it is common practice to only include optical variables that represent light which is captured by the projection lens, but when variables in the object plane are used they will generally include at least some light components that the lens cannot capture.
For clarity, any optimization involving optical variables will be referred to here as an optical domain optimization, regardless of whether this light includes components that are not collected by the lens. Further, the optical domain optimization can be referred to here as pupil domain when the optical variables are defined as the pupil amplitudes, and can be referred to here as object domain when the optical variables are defined at the mask exit. When mask polygons are optimized instead of optical variables, which in some conventions can be regarded as a spatial domain optimization, the term polygon domain optimization will be used.
The ILT technologies can contribute design manufacturability of the optical mask in the state of the art implementations; however, the ILT has some defects in the optimization of mask topology. FIG. 10 shows a plot of computation time and objective values of ruling (both in arbitrary units) and mask sampling rates (in arbitrary unit); the left hand ordinate represents the objective value; the right hand ordinate represents the computation time; the abscissa represents the sampling rate of the mask pixels.
Referring to FIG. 10, the ILT improves the objective value as the sampling rates of the pixels increase; however, the computation time for obtaining the corresponding objective values increases in a worse than linear relation with respect to the sampling rate, while the improvement in the objective value slows down in a likewise worse than linear relation to that of the computation time as well as to total runtime.
When object domain sampling is made at points on a coarse grid, corresponding to a low sampling rate, the solution cannot achieve the sharp edges that are needed to produce patterned images of the highest possible contrast. In the particular case where the coarsely spaced mask variables take the form of finite pixels within a coarse gridding, it does become possible for the mask edges to become sharply defined; however in this case the sharp mask edges occurring at the boundaries of coarsely sized pixels will usually not be accurately positioned at the location where sharp mask edges are needed, or, more precisely, when sharp edges occur at the boundaries of coarsely sized pixels they will usually not produce image edges at exactly the right locations.
Further, it is common practice in the prior art to bring the finished optical domain solution closer to manufacturability by rounding its transmission values to the levels supported by the mask technology, such as 0 and 1 for so-called binary masks. When such a rounding post-processing is employed in ILT, it is common to add terms to the objective that promote pixel transmission values which come close to the supported values during the optimization. However, it is also important that the transmission of small assisting features remain too dim to print, while at the same time remaining bright enough to provide optical benefit, for example by improving the stability of the image in the face of focus fluctuations.
Unfortunately, when coarse pixels of intermediate transmission are rounded during post-processing, they can either be raised in transmission to a level that prints as an artifact, or they can be rounded down to the transmission level of the mask blank background, eliminating their optical benefit. It becomes possible for assisting features to avoid this problem if very finely spaced pixels are used, in that the pixels can have a width that is much narrower than the lens resolution, along with a high peak transmission that survives rounding, so that the lens reduces their intensity below the print threshold when blurring out their image to a width comparable to the lens resolution. For these reasons, fine spacing during optical domain optimization can allow high quality mask solutions to be obtained, as shown in FIG. 11. However, the number of variables increases quadratically as the variable spacing decreases, and computation speed generally degrades at least linearly with the number of variables, and usually degrades more rapidly than linearly. Therefore, the conventional ILT can not provide a scalability of designing the mask for the state of the art predetermined objective value and requires increasing computation performance with respect to the objective values of the ruling.
Different mask design techniques are disclosed in JPA 2010-140020 and JPA 2010-140021 based on selection of edge pairs including the conventional nonlinear problem solver which evaluates manufacturability of the mask.
As described above, an object of the present invention is to provide a novel mask design technology which enables scalability of topology computation while reducing computation time and hardware resources.
Another object of the present invention is to provide a novel mask design technology which allows modification of mask topology within acceptable ranges during the optimization cycles.
Another object of the present invention is to provide a mask design method, a program therefore, and a mask design system which ensure the scalability of the topology computation by allowing modification of mask topology within acceptable ranges during the optimization cycles while reducing the computation time and hardware resources.